Optimality, Equilibrium, and Curb Sets in Decision Problems Without Commitment
Maastricht University, School of Business and Economics, RM/16/021
19 Pages Posted: 28 May 2016
Date Written: May 10, 2016
Abstract
The paper considers a class of decision problems with in_nite time horizon that contains Markov decision problems as an important special case. Our interest concerns the case where the decision maker cannot commit himself to his future action choices. We model the decision maker as consisting of multiple selves, where each history of the decision problem corresponds to one self. Each self is assumed to have the same utility function as the decision maker. We introduce the notions of Nash equilibrium, subgame perfect equilibrium, and curb sets for decision problems. An optimal policy at the initial history is a Nash equilibrium but not vice versa. Both subgame perfect equilibria and curb sets are equivalent to subgame optimal policies. The concept of a subgame optimal policy is therefore robust to the absence of commitment technologies.
Keywords: decision problem, multiple selves, subgame perfect equilibrium, curb sets
JEL Classification: C61, C62, C73
Suggested Citation: Suggested Citation